I'm not sure what you meant about not using real ISBNs. There is only one definition of, and provider for ISBNs, and they do use them according to the FAQs.
As far as being available to other stores, that's where POD publishing is getting trickier, especially in light of the new Amazon situation. Until this new development, if you went with most of the POD publishers, your book would be eligible to be ordered through Ingram outlets (bookstores) and Amazon because companies could have relationships with both.
Now though, assuming the changes stick, you'll have to set up with Booksurge/maybe Create Space or whoever else signs the contract, to access Amazon, and another POD to access Ingram. Should be doable if you own your own ISBN. You'll basically have two resources for production into the two supply chains.
Now, it appears things are complicated even more if you use a Createspace ISBN instead because I don't believe they would release it to you to use with another production source/publisher. Most PODs do not do that now, so it makes sense that they wouldn't either. That would mean to me that you'd be limited to distribution through Amazon and your own website.
Stuff like this is just one of the reasons authors really need to educate themselves well about the industry before agreeing to do anything with anyone. POD can be quite confusing, and it doesn't look like it's going to get any easier anytime soon.
Sorry if this is short story long, hope it answers things for you.